As explained by Matt Bellamy and inferred by the title, this song (“Won’t Stand Down”) is based on the notion of refusing to “stand down” to a bully. And more macrocosmically, said bully can be theoretically interpreted as being the system or powers-that-be itself.
But by the time all is said and done, the lyrics honestly sound very much personal. Moreover, as far as the actual verses go, it doesn’t really come off as if the vocalist is addressing a bully. Instead said individual(s) is presented more overtly as a “user and abuser”, or for the sake of simplicity let’s say a former friend who has proven to be sheisty.
At first, as such situations tend to go, the vocalist wasn’t able to pick up on this fact. But somewhere along the line he has come to the realization that the addressee has been ‘stringing him along’, as in using him in one way or another. So now, after realizing this, the singer sounds quite vengeful.
Or put differently, he’s committed to righting the wrongs inflicted on him – not in a general sort of way but directly against the addressee himself. In fact the chorus even concludes with the phrase “die alone”, which is obviously also directed at this individual.
So the thesis sentiment can be deemed as the vocalist celebrating the fact that he “won’t stand down” to the addressee upon the realization that the latter is exploitative.
All explanations considered, the implication would be that the singer realized this previously but only now has mustered up the heart to confront the matter, which is the reason why he’s celebratory. And in the process of resisting the addressee, he has also ‘grown stronger’. And perhaps most pointedly, his ultimate goal with this newfound strength is to get revenge against the person who offended him.